Question 1

Suppose a firm's production function is given by $$Q = L K^2$, where L$ is labor and K$ is capital. In the short run, capital is fixed at K = 10$. If the price of labor is w = 2$ and the price of capital is r = 5$, what is the formula for the firm's total cost C$ as a function of output Q$?

Accepted Answer

$$C = 2 \frac{Q}{K^2$} + 5K$$

Question 2

Given the production function $$Q = L K^2$ with K = 10$ in the short run, and input prices w = 2$, r = 5$, what is the formula for the variable cost (VC) as a function of output Q$?

Accepted Answer

$$VC = 2 \frac{Q}{100}$$

Question 3

For the same firm as above, what is the formula for the fixed cost (FC) in the short run?

Accepted Answer

$$FC = 5K$$

Question 4

If the wage rate $$w = 10$$ and the rental rate of capital $$r = 5$$, what is the slope of an isocost line?

Accepted Answer

$$-2$$

Question 5

Suppose a firm faces input prices $$w = 5$$ and $$r = 10. If $$the firm wants to minimize the cost of producing a given output, which condition must be satisfied at the optimal input combination?

Accepted Answer

$$\frac{MP_L}{w} = \frac{MP_K}{r}$$

Question 6

If the price of capital ($$r) $$increases, what happens to the least-cost combination of labor ($$L) $$and capital ($$K) $$for producing a given output $$Q$$?

Accepted Answer

The firm will use less capital and more labor.

Question 7

Given the isocost equation $$C = wL + rK$$, if $$C = 100$$, $$w = 10$$, and $$r = 5$$, what is the intercept of the isocost line on the $$K-$$axis?

Accepted Answer

$$K = 20$$

Question 8

Suppose a firm’s isoquant for $$Q = 2 is $$tangent to an isocost line at $$L = 7$$ and $$K = 7. If$$ $$w = 5$$ and $$r = 10$$, what is the total cost of producing $$Q = 2$$?

Accepted Answer

$$C = 105$$

Question 9

If a firm’s production function exhibits increasing returns to scale, what happens to average cost as output increases?

Accepted Answer

Average cost decreases.

Question 10

A firm’s marginal cost (MC) is given by $$MC = \frac{dC}{dQ}. If $$the total cost function is $$C(Q) = 50 + 2Q$$, what is the marginal cost?

Accepted Answer

$$MC = 2$$

Question 11

Suppose a firm’s average fixed cost (AFC) is $$AFC = \frac{FC}{Q}. If $$fixed cost is $$FC = 50$$ and output is $$Q = 5$$, what is the average fixed cost?

Accepted Answer

$$AFC = 10$$

Question 12

If a firm’s total cost is $$C = 50 + 2Q$$ and output increases from $$Q = 2 to$$ $$Q = 3$$, what is the marginal cost for this increase?

Accepted Answer

$$MC = 2$$

Question 13

In the long run, all inputs are variable. If a firm wants to produce output $$Q at $$the lowest cost, which of the following must be true at the optimal input combination?

Accepted Answer

$$\frac{MP_L}{w} = \frac{MP_K}{r}$$

Question 14

If the isocost line becomes steeper due to an increase in the price of capital, what does this indicate about the relative prices of labor and capital?

Accepted Answer

Capital has become relatively more expensive than labor.

Question 15

Suppose a firm’s cost function is $$C(Q) = 50 + 2Q. $$What is the average cost (AC) when $$Q = 5$$?

Accepted Answer

$$AC = 12$$

Question 16

If a firm’s isoquant for $$Q = 3 is $$tangent to an isocost line at $$L = 8$$ and $$K = 7$$, with $$w = 5$$ and $$r = 10$$, what is the total cost of producing $$Q = 3$$?

Accepted Answer

$$C = 120$$

Question 17

Which of the following best describes an isoquant?

Accepted Answer

A curve showing all combinations of inputs that yield the same output.

Question 18

If a firm’s isocost line shifts outward (parallel to the original), what does this indicate?

Accepted Answer

The firm can now afford more of both inputs at the same prices.

Question 19

Suppose a firm’s marginal cost (MC) is constant and equal to $$2. If $$the firm’s fixed cost is $$50$$, what is the total cost of producing $$Q$$ units?

Accepted Answer

$$C = 2Q + 50$$

Microeconomics Cost and Production Analysis Study Guide

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